en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 8/x-5e^x

Solution

\int \frac{8}{x} - 5 e^{x} d x

Solution

8 ln ∣ x ∣ - 5 e^{x} + C

Solution steps

\int \frac{8}{x} - 5 e^{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{8}{x} d x - \int 5 e^{x} d x

\int \frac{8}{x} d x = 8 ln ∣ x ∣

\int 5 e^{x} d x = 5 e^{x}

= 8 ln ∣ x ∣ - 5 e^{x}

Add a constant to the solution

= 8 ln ∣ x ∣ - 5 e^{x} + C

Graph

Popular Examples

integral of (7x)/(5x^2-3)

\int \frac{7 x}{5 x ^{2} - 3} d x

integral of ((-7)/x+e^{9x}+9/4)

\int (\frac{- 7}{x} + e^{9 x} + \frac{9}{4}) d x

integral of 2xcos(x^2+1)

\int 2 x cos (x^{2} + 1) d x

integral of ()(e^{2t}x)

\int \frac{d}{d t} (e^{2 t} x) d t

integral of x(x^2+3)^8

\int x (x^{2} + 3)^{8} d x

Frequently Asked Questions (FAQ)

What is the integral of 8/x-5e^x ?
The integral of 8/x-5e^x is 8ln|x|-5e^x+C